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The number of fish in the lake follows an arithmetic sequence
The number of fish in the lake the second year is 7800, and it is represented by f(2)
The model of the number of fish is given as:
[tex]\mathbf{f(n + 1) = f(n) - 400}[/tex]
Such that:
[tex]\mathbf{f(1) = 8200}[/tex]
Set n = 1, to calculate f(2)
Substitute 1 for n in the given model [tex]\mathbf{f(n + 1) = f(n) - 400}[/tex]
So, we have:
[tex]\mathbf{f(n + 1) = f(n) - 400}[/tex]
[tex]\mathbf{f(1 + 1) = f(1) - 400}[/tex]
Simplify, by adding 1 and 1
[tex]\mathbf{f(2) = f(1) - 400}[/tex]
Substitute 8200 for f(1)
[tex]\mathbf{f(2) = 8200 - 400}[/tex]
Subtract 400 from 8200
[tex]\mathbf{f(2) = 7800}[/tex]
Hence, the value of f(2) is 7800
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